Algebra Lab - Comparison of Car Fuel Economy
by Lynn Onken
This is a study of the fuel economy rates for two different vehicles and the cost of fuel for each over a given time period.
Comprehension
Observations regarding the fuel economy of an automobile, designing a model of the relationship of miles and gallons consumed
Questions
- You may have observed the cost of fuel has been increasing over the last few years. There are problems associated with the amount of fuel each vehicle uses, as well as the cost to the owner. List some of them now.
- Amount of fuel used when driving different vehicles may be one of the items you observed. Specifically, what do you think the relationship between driving a four-cylinder vehicle and an eight-cylinder vehicle is, in terms of the amount of fuel consumed
- What happens when most of the community drives vehicles that consume a lot of fuel?
- Who benefits from the use of vehicles that consume a lot of fuel?
- If you answered the previous question with “gasoline companies”, you are right. How does a consumer drive a vehicle in the most economical way?
- What effect does the consumption of a great amount of fuel have on our environment? Why?
Acquisition
Mathematical Topics
Learn or review mathematical concepts and skills needed to study car fuel economy. See the menu at the left.
Automobiles: Part I
Information
Suppose you own a Ford Contour, four-cylinder vehicle. You are interested in finding out the average fuel economy for your vehicle, so you keep track of the miles you have driven, and the amount of fuel you have used each time you get gas. The table below provides the data you have recorded for a time period, the first column noting the number of miles driven between fill-ups and the second column indicating the number of gallons purchased.
Data Table
Miles Driven Gallons 262 10.25 301 11.80 347 11.60 272 10.50 368 12.08 293 10.08 Application
Apply mathematical knowledge and Tool Chest applets to analyze the rate of fuel consumption by the Contour. Analyze the cost of fuel for the car over a period of time.
Questions
- Make points from the data in the table, one for each record. The first coordinate will be the miles driven and the second coordinate will be the number of gallons used.
- Using the linear regression applet, plot the points for these records. What does the data appear to do? Why do you think the graph looks like this?
- Using the linear regression applet, find the model of best fit. What is the value of the coefficient of x? What does this value represent to you, the car owner.
- If you traveled an average of 500 miles each month for an entire year, how many gallons of gas do you think you will use?
- If every member of a five-person family drove an average of 500 miles each month, assuming all drove cars with similar gas consumption as the Contour, how much gasoline would be needed?
- Estimate the amount of gasoline you will need for a 2000-mile trip.
- Find the rate of change (slope) for a 1500-mile trip and the 2000-mile trip. Compare this to the coefficient of x in your linear model.
Reflection
Examine solutions and implications.
- Do you think the model you found accurately reflects the data?
- Will the model always work? In what situations would the model become invalid? For what length of time will the model remain valid?
- Why is it important to keep records of your fuel consumed and miles driven?
- What benefit will this information be to you? How can you use the information to your advantage?
Automobiles: Part II
Comprehension
Observations regarding the fuel economy of an automobile, designing a comparison of two different vehicles, the amount of fuel used by each.
Questions
- You may have observed the cost of fuel has been increasing over the last few years. There are problems associated with the amount of fuel each vehicle uses, as well as the cost to the owner. List some of them now.
- Amount of fuel used when driving different vehicles may be one of the items you observed. Specifically, what do you think the relationship between driving a four-cylinder vehicle and an eight-cylinder vehicle is, in terms of the amount of fuel consumed?
- What happens when most of the community drives vehicles that consume a lot of fuel?
- Who benefits from the use of vehicles that consume a lot of fuel?
- If you answered the previous question with “gasoline companies”, you are right. How does a consumer drive a vehicle in the most economical way?
- What effect does the consumption of a great amount of fuel have on our environment? Why?
Acquisition
Mathematical Topics
Learn or review mathematical concepts and skills needed to study car fuel economy. See the menu at the left.
Information
Automobiles
Suppose you are considering owning a Chevrolet Impala, an eight-cylinder vehicle. You currently own a Ford Contour, a four-cylinder vehicle. You are interested in finding out the average fuel economy for the new vehicle, A friend owns an Impala, so you obtain records from her including the number of the miles they have driven, and the amount of fuel they have used for these miles. The table below provides the data you have recorded by your friend when they first purchased the Impala.
Cumulative Data Table
Miles Gallons 3072 208.37 1966 108.40 740 44.06 809 48.06 991 58.60 821 46.15 1159 66.48 Application
Apply mathematical knowledge and Tool Chest applets to analyze the rate of fuel consumption of the Impala. Analyze the cost of fuel for the car over a period of time.
Questions
- Make points from the data in the table, one for each record. The first coordinate will be the miles driven and the second coordinate will be the number of gallons used.
- Using the linear regression applet, plot the points for these records. What does the data appear to do? Why do you think the graph looks like this?
- Using the linear regression applet, find the model of best fit. What is the value of the coefficient of x? What does this value represent to you, the car owner.
- If you traveled an average of 500 miles each month for an entire year, how many gallons of gas do you think you will use?
- If every member of a five-person family drove an average of 500 miles each month, assuming all drove cars with similar gas consumption as the Contour, how much gasoline would be needed?
- Estimate the amount of gasoline you will need for a 2000-mile trip.
- Find the rate of change (slope) for a 1500-mile trip and the 2000-mile trip. Compare this to the coefficient of x in your linear model.
Reflection
Examine solutions and implications.
- Do you think the model you found accurately reflect the data on the Impala?
- Will the models always work? In what situations would the model become invalid? For what length of time will the model remain valid?
- Why is it important to keep records of your fuel consumed and miles driven?
- What benefit will this information be to you? How can you use the information to your advantage? If you completed the Part I models for the Contour as well:
- How do the results for the Impala compare to the results for the Contour?
- If you drove the Impala for a year, how different will your fuel consumption be when compared to the Contour?
- What would be the benefits to driving either vehicle? What would be the negative aspects, particularly if you were to take a long trip?
